The problem requires simplifying various expressions involving exponents, multiplication, and division. We have 20 expressions to simplify.

1. Problem Description

The problem requires simplifying various expressions involving exponents, multiplication, and division. We have 20 expressions to simplify.

2. Solution Steps

1. $10^5 \times 10^4 = 10^{5+4} = 10^9$

2. $a^3 \times a^9 = a^{3+9} = a^{12}$

3. $5y \times 4y^4 = (5 \times 4) \times (y \times y^4) = 20y^{1+4} = 20y^5$

4. $2^2 \times 2^4 = 2^{2+4} = 2^6 = 64$

5. $m^8 \div m^5 = m^{8-5} = m^3$

6. $c^7 \div c = c^7 \div c^1 = c^{7-1} = c^6$

7. $\frac{24x^6}{8x^4} = \frac{24}{8} \times \frac{x^6}{x^4} = 3 \times x^{6-4} = 3x^2$

8. $\frac{9 \times 10^9}{3 \times 10^3} = \frac{9}{3} \times \frac{10^9}{10^3} = 3 \times 10^{9-3} = 3 \times 10^6 = 3,000,000$

9. $2^0 = 1$ (Anything to the power of zero is 1.)

1

0. $6 \times z^0 = 6 \times 1 = 6$

1

1. $4^{-3} = \frac{1}{4^3} = \frac{1}{4 \times 4 \times 4} = \frac{1}{64}$

1

2. $3x^{-3} = 3 \times \frac{1}{x^3} = \frac{3}{x^3}$

1

3. $(1-4)^{-2} = (-3)^{-2} = \frac{1}{(-3)^2} = \frac{1}{(-3) \times (-3)} = \frac{1}{9}$

1

4. $(2-3)^{-1} = (-1)^{-1} = \frac{1}{-1} = -1$

1

5. $x^3 \div x^{-5} = x^{3 - (-5)} = x^{3+5} = x^8$

1

6. $a^{-9} \div b^0 = a^{-9} \div 1 = a^{-9} = \frac{1}{a^9}$

1

7. $(3x)^{-3} = 3^{-3} \times x^{-3} = \frac{1}{3^3} \times \frac{1}{x^3} = \frac{1}{27} \times \frac{1}{x^3} = \frac{1}{27x^3}$

1

8. $9a^{-5} \times 4a^6 = (9 \times 4) \times (a^{-5} \times a^6) = 36 \times a^{-5+6} = 36a^1 = 36a$

1

9. $5x^2 \times 4x^0 \times 2x^{-6} = (5 \times 4 \times 2) \times (x^2 \times x^0 \times x^{-6}) = 40 \times x^{2+0-6} = 40x^{-4} = \frac{40}{x^4}$

2

0. $15 \times 10^4 \div (3 \times 10^{-2}) = \frac{15 \times 10^4}{3 \times 10^{-2}} = \frac{15}{3} \times \frac{10^4}{10^{-2}} = 5 \times 10^{4-(-2)} = 5 \times 10^{4+2} = 5 \times 10^6 = 5,000,000$

3. Final Answer

1. $10^9$

2. $a^{12}$

3. $20y^5$

4. $64$

5. $m^3$

6. $c^6$

7. $3x^2$

8. $3,000,000$

9. $1$

1

0. $6$

1

1. $\frac{1}{64}$

1

2. $\frac{3}{x^3}$

1

3. $\frac{1}{9}$

1

4. $-1$

1

5. $x^8$

1

6. $\frac{1}{a^9}$

1

7. $\frac{1}{27x^3}$

1

8. $36a$

1

9. $\frac{40}{x^4}$

2

0. $5,000,000$